Question

There are currently 17 frogs in a (large) pond. The frog population grows exponentially, tripling every 6 days. How long will it take (in days) for there to be 130 frogs in the pond? Round your answer to the nearest hundredth.

Answer 1

t=11,11 days

Explanation:

F=frogs poblation, t=time, be the variables dF/dt = KF, dF/F=Kdt, integrating
`\int\limits^ {} \, dF/F =K\int\limits^ {} \, dt`⇒ LnF=Kt+c,
`F=ce^(Kt)`; Knowing t=0, F=17 and t=6 F=51 (tripling every 6 days (17*3)),
`F=ce^(K0) = F=c=17; F=17e^(6K) =51`⇒
`e^(6K) =51/17; K6=ln(51)/(17) ; K=ln(51)/(17)/6=0.183`, so
`F=17e^(0,183t)`, now if F=130, t=? we have:

`130=17e^(0.183t) =e^(0.183t) =130/17; 0.183t=ln(130/17); t=ln(130/17)/0.183 = 11,11`